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Reconstruction Of Small Inhomogeneities From Boundary Measurements
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Book Synopsis Reconstruction of Small Inhomogeneities from Boundary Measurements by : Habib Ammari
Download or read book Reconstruction of Small Inhomogeneities from Boundary Measurements written by Habib Ammari and published by Springer. This book was released on 2004-08-30 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.
Book Synopsis Reconstruction of Small Inhomogeneities from Boundary Measurements by : Habib Ammari
Download or read book Reconstruction of Small Inhomogeneities from Boundary Measurements written by Habib Ammari and published by . This book was released on 2014-01-15 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Inverse Problems, Multi-Scale Analysis, and Effective Medium Theory by : Habib Ammari
Download or read book Inverse Problems, Multi-Scale Analysis, and Effective Medium Theory written by Habib Ammari and published by American Mathematical Soc.. This book was released on 2006 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent developments in inverse problems, multi-scale analysis and effective medium theory reveal that these fields share several fundamental concepts. This book is the proceedings of the research conference, ``Workshop in Seoul: Inverse Problems, Multi-Scale Analysis and Homogenization,'' held at Seoul National University, June 22-24, 2005. It highlights the benefits of sharing ideas among these areas, of merging the expertise of scientists working there, and of directing interest towards challenging issues such as imaging nanoscience and biological imaging. Contributions are written by prominent experts and are of interest to researchers and graduate students interested in partial differential equations and applications.
Book Synopsis Partial Differential Equations and Inverse Problems by : Carlos Conca
Download or read book Partial Differential Equations and Inverse Problems written by Carlos Conca and published by American Mathematical Soc.. This book was released on 2004 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is a collection of articles from the Pan-American Advanced Studies Institute on partial differential equations, nonlinear analysis and inverse problems held in Santiago (Chile). Interactions among partial differential equations, nonlinear analysis, and inverse problems have produced remarkable developments over the last couple of decades. This volume contains survey articles reflecting the work of leading experts who presented minicourses at the event. Contributors include J. Busca, Y. Capdeboscq, M.S. Vogelius, F. A. Grunbaum, L. F. Matusevich, M. de Hoop, and P. Kuchment. The volume is suitable for graduate students and researchers interested in partial differential equations and their applications in nonlinear analysis and inverse problems.
Book Synopsis Mathematical Modeling in Biomedical Imaging I by : Habib Ammari
Download or read book Mathematical Modeling in Biomedical Imaging I written by Habib Ammari and published by Springer Science & Business Media. This book was released on 2009-10-21 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume gives an introduction to a fascinating research area to applied mathematicians. It is devoted to providing the exposition of promising analytical and numerical techniques for solving challenging biomedical imaging problems, which trigger the investigation of interesting issues in various branches of mathematics.
Book Synopsis An Elastic Model for Volcanology by : Andrea Aspri
Download or read book An Elastic Model for Volcanology written by Andrea Aspri and published by Springer Nature. This book was released on 2019-11-08 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a rigorous mathematical framework for a linear elastic model arising from volcanology that explains deformation effects generated by inflating or deflating magma chambers in the Earth’s interior. From a mathematical perspective, these modeling assumptions manifest as a boundary value problem that has long been known by researchers in volcanology, but has not, until now, been given a thorough mathematical treatment. This mathematical study gives an explicit formula for the solution of the boundary value problem which generalizes the few well-known, explicit solutions found in geophysics literature. Using two distinct analytical approaches—one involving weighted Sobolev spaces, and the other using single and double layer potentials—the well-posedness of the elastic model is proven. An Elastic Model for Volcanology will be of particular interest to mathematicians researching inverse problems, as well as geophysicists studying volcanology.
Book Synopsis Layer Potential Techniques in Spectral Analysis by : Habib Ammari
Download or read book Layer Potential Techniques in Spectral Analysis written by Habib Ammari and published by American Mathematical Soc.. This book was released on 2009 with total page 211 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the early part of the twentieth century, the use of integral equations has developed into a range of tools for the study of partial differential equations. This includes the use of single- and double-layer potentials to treat classical boundary value problems. The aim of this book is to give a self-contained presentation of an asymptotic theory for eigenvalue problems using layer potential techniques with applications in the fields of inverse problems, band gap structures, and optimal design, in particular the optimal design of photonic and phononic crystals. Throughout this book, it is shown how powerful the layer potentials techniques are for solving not only boundary value problems but also eigenvalue problems if they are combined with the elegant theory of Gohberg and Sigal on meromorphic operator-valued functions. The general approach in this book is developed in detail for eigenvalue problems for the Laplacian and the Lame system in the following two situations: one under variation of domains or boundary conditions and the other due to the presence of inclusions. The book will be of interest to researchers and graduate students working in the fields of partial differential equations, integral equations, and inverse problems. Researchers in engineering and physics may also find this book helpful.
Book Synopsis Handbook of Mathematical Methods in Imaging by : Otmar Scherzer
Download or read book Handbook of Mathematical Methods in Imaging written by Otmar Scherzer and published by Springer Science & Business Media. This book was released on 2010-11-23 with total page 1626 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Mathematical Methods in Imaging provides a comprehensive treatment of the mathematical techniques used in imaging science. The material is grouped into two central themes, namely, Inverse Problems (Algorithmic Reconstruction) and Signal and Image Processing. Each section within the themes covers applications (modeling), mathematics, numerical methods (using a case example) and open questions. Written by experts in the area, the presentation is mathematically rigorous. The entries are cross-referenced for easy navigation through connected topics. Available in both print and electronic forms, the handbook is enhanced by more than 150 illustrations and an extended bibliography. It will benefit students, scientists and researchers in applied mathematics. Engineers and computer scientists working in imaging will also find this handbook useful.
Book Synopsis Topological Optimization and Optimal Transport by : Maïtine Bergounioux
Download or read book Topological Optimization and Optimal Transport written by Maïtine Bergounioux and published by Walter de Gruyter GmbH & Co KG. This book was released on 2017-08-07 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: By discussing topics such as shape representations, relaxation theory and optimal transport, trends and synergies of mathematical tools required for optimization of geometry and topology of shapes are explored. Furthermore, applications in science and engineering, including economics, social sciences, biology, physics and image processing are covered. Contents Part I Geometric issues in PDE problems related to the infinity Laplace operator Solution of free boundary problems in the presence of geometric uncertainties Distributed and boundary control problems for the semidiscrete Cahn–Hilliard/Navier–Stokes system with nonsmooth Ginzburg–Landau energies High-order topological expansions for Helmholtz problems in 2D On a new phase field model for the approximation of interfacial energies of multiphase systems Optimization of eigenvalues and eigenmodes by using the adjoint method Discrete varifolds and surface approximation Part II Weak Monge–Ampere solutions of the semi-discrete optimal transportation problem Optimal transportation theory with repulsive costs Wardrop equilibria: long-term variant, degenerate anisotropic PDEs and numerical approximations On the Lagrangian branched transport model and the equivalence with its Eulerian formulation On some nonlinear evolution systems which are perturbations of Wasserstein gradient flows Pressureless Euler equations with maximal density constraint: a time-splitting scheme Convergence of a fully discrete variational scheme for a thin-film equatio Interpretation of finite volume discretization schemes for the Fokker–Planck equation as gradient flows for the discrete Wasserstein distance
Book Synopsis IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials by : Martin Philip Bendsoe
Download or read book IUTAM Symposium on Topological Design Optimization of Structures, Machines and Materials written by Martin Philip Bendsoe and published by Springer Science & Business Media. This book was released on 2006-10-03 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers edited papers presented at the IUTAM-Symposium Topological design optimization of structures, machines and materials - status and perspectives, October 2005. The papers cover the application of topological design optimization to fluid-solid interaction problems, acoustics problems, and to problems in biomechanics, as well as to other multiphysics problems. Also in focus are new basic modelling paradigms, covering new geometry modelling such as level-set methods and topological derivatives.
Book Synopsis Mathematical and Statistical Methods for Imaging by : Habib Ammari
Download or read book Mathematical and Statistical Methods for Imaging written by Habib Ammari and published by American Mathematical Soc.. This book was released on 2011-07-20 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the NIMS Thematic Workshop on Mathematical and Statistical Methods for Imaging, which was held from August 10-13, 2010, at Inha University, Incheon, Korea. The goal of this volume is to give the reader a deep and unified understanding of the field of imaging and of the analytical and statistical tools used in imaging. It offers a good overview of the current status of the field and of directions for further research. Challenging problems are addressed from analytical, numerical, and statistical perspectives. The articles are devoted to four main areas: analytical investigation of robustness; hypothesis testing and resolution analysis, particularly for anomaly detection; new efficient imaging techniques; and the effects of anisotropy, dissipation, or attenuation in imaging.
Book Synopsis Inverse Problems and Spectral Theory by : Hiroshi Isozaki
Download or read book Inverse Problems and Spectral Theory written by Hiroshi Isozaki and published by American Mathematical Soc.. This book was released on 2004 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume grew out of a workshop on spectral theory of differential operators and inverse problems held at the Research Institute for Mathematical Sciences (Kyoto University). The gathering of nearly 100 participants at the conference suggests the increasing interest in this field of research. The focus of the book is on spectral theory for differential operators and related inverse problems. It includes selected topics from the following areas: electromagnetism, elasticity, the Schrodinger equation, differential geometry, and numerical analysis. The material is suitable for graduate students and researchers interested in inverse problems and their applications.
Book Synopsis Theory and Applications of Applied Electromagnetics by : Ping Jack Soh
Download or read book Theory and Applications of Applied Electromagnetics written by Ping Jack Soh and published by Springer. This book was released on 2016-07-04 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, experts from academia and industry present the latest advances in scientific theory relating to applied electromagnetics and examine current and emerging applications particularly within the fields of electronics, communications, and computer technology. The book is based on presentations delivered at APPEIC 2015, the 2nd Applied Electromagnetic International Conference, held in Krabi, Thailand in December 2015. The conference provided an ideal platform for researchers and specialists to deliver both theoretically and practically oriented contributions on a wide range of topics relevant to the theme of nurturing applied electromagnetics for human technology. Many novel aspects were addressed, and the contributions selected for this book highlight the relevance of advances in applied electromagnetics to a variety of industrial engineering problems and identify exciting futu re directions for research.
Book Synopsis Direct and Inverse Problems in Wave Propagation and Applications by : Ivan Graham
Download or read book Direct and Inverse Problems in Wave Propagation and Applications written by Ivan Graham and published by Walter de Gruyter. This book was released on 2013-10-14 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the third volume of three volume series recording the "Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment" taking place in Linz, Austria, October 3-7, 2011. This book surveys recent developments in the analysis of wave propagation problems. The topics covered include aspects of the forward problem and problems in inverse problems, as well as applications in the earth sciences. Wave propagation problems are ubiquitous in environmental applications such as seismic analysis, acoustic and electromagnetic scattering. The design of efficient numerical methods for the forward problem, in which the scattered field is computed from known geometric configurations is very challenging due to the multiscale nature of the problems. Even more challenging are inverse problems where material parameters and configurations have to be determined from measurements in conjunction with the forward problem. This book contains review articles covering several state-of-the-art numerical methods for both forward and inverse problems. This collection of survey articles focusses on the efficient computation of wave propagation and scattering is a core problem in numerical mathematics, which is currently of great research interest and is central to many applications in energy and the environment. Two generic applications which resonate strongly with the central aims of the Radon Special Semester 2011 are forward wave propagation in heterogeneous media and seismic inversion for subsurface imaging. As an example of the first application, modelling of absorption and scattering of radiation by clouds, aerosol and precipitation is used as a tool for interpretation of (e.g.) solar, infrared and radar measurements, and as a component in larger weather/climate prediction models in numerical weather forecasting. As an example of the second application, inverse problems in wave propagation in heterogeneous media arise in the problem of imaging the subsurface below land or marine deposits. The book records the achievements of Workshop 3 "Wave Propagation and Scattering, Inverse Problems and Applications in Energy and the Environment". It brings together key numerical mathematicians whose interest is in the analysis and computation of wave propagation and scattering problems, and in inverse problems, together with practitioners from engineering and industry whose interest is in the applications of these core problems.
Book Synopsis Multi-wave Medical Imaging: Mathematical Modelling And Imaging Reconstruction by : Nguyen Loc Hoang
Download or read book Multi-wave Medical Imaging: Mathematical Modelling And Imaging Reconstruction written by Nguyen Loc Hoang and published by World Scientific. This book was released on 2017-03-03 with total page 688 pages. Available in PDF, EPUB and Kindle. Book excerpt: Super-Resolution imaging refers to modern techniques of achieving resolution below conventional limits. This book gives a comprehensive overview of mathematical and computational techniques used to achieve this, providing a solid foundation on which to develop the knowledge and skills needed for practical application of techniques. Split into five parts, the first looks at the mathematical and probabilistic tools needed, before moving on to description of different types of imaging; single-wave, anomaly, multi-wave and spectroscopic and nanoparticle. As an important contribution to the understanding of super-resolution techniques in biomedical imaging, this book is a useful resource for scientists and engineers in the fields of biomedical imaging and super-resolution, and is self-contained reference for any newcomers to these fields.
Book Synopsis Reconstruction of Small Inhomogeneities from Boundary Measurements by : Habib Ammari
Download or read book Reconstruction of Small Inhomogeneities from Boundary Measurements written by Habib Ammari and published by Springer. This book was released on 2004-08-03 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first book to provide a systematic exposition of promising techniques for the reconstruction of small inhomogeneities from boundary measurements. In particular, theoretical results and numerical procedures for the inverse problems for the conductivity equation, the Lamé system, as well as the Helmholtz equation are discussed in a readable and informative manner. The general approach developed in this book is based on layer potential techniques and modern asymptotic analysis of partial differential equations. The book is particularly suitable for graduate students in mathematics.
Book Synopsis Imaging, Multi-scale and High Contrast Partial Differential Equations by : Habib Ammari
Download or read book Imaging, Multi-scale and High Contrast Partial Differential Equations written by Habib Ammari and published by American Mathematical Soc.. This book was released on 2016-03-23 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Seoul ICM 2014 Satellite Conference on Imaging, Multi-scale and High-Contrast PDEs, held from August 7-9, 2014, in Daejeon, Korea. The mathematical analysis of partial differential equations modelling materials, or tissues, presenting multiple scales has been a very active area of research. The study of the corresponding imaging or reconstruction problem is a more recent area. If the material parameters of the partial differential equation present high contrast ratio, then the solution to the PDE becomes particularly challenging to analyze and compute. On the other hand, imaging in highly heterogeneous media poses significant challenges to the mathematical community. The focus of this volume is on recent progress towards complete understanding of the direct problem with high contrast or high frequencies, and unified approaches to the inverse and imaging problems for both small and large contrast or frequencies. Of particular importance in imaging are shape representation techniques and regularization approaches. Special attention is devoted to new models and problems coming from physics leading to innovative imaging and signal processing methods.
